Rational Functions and Asymptotes

Consider the rational function given by two polynomial functions;

What about these two polynomials decides the location of:

• The vertical asymptotes?
• The horizontal asymptotes?
• The solutions to f(x)=0?

I know the theory behind this, but what does it look like in motion?

The geogebra file linked here https://www.geogebra.org/m/m8eqsjzu explores this. What happens as I click and drag one of the curves? How does it make the graph of f(x) move?

Introducing Complex Numbers

 I was watching an old OU video and there was a demonstration there that needed an update to geogebra - no need for hand animation any more!

The geogebra file is https://www.geogebra.org/m/waggbjrr here!

The file allows you to take a polynomial curve and see what happens to the solution set as you move the curve vertically, demonstrating what happens to those roots in the complex plane.